Motor response vigour and visual fixation patterns reflect subjective valuation during intertemporal choice

Value-based decision-making is of central interest in cognitive neuroscience and psychology, as well as in the context of neuropsychiatric disorders characterised by decision-making impairments. Studies examining (neuro-)computational mechanisms underlying choice behaviour typically focus on participants’ decisions. However, there is increasing evidence that option valuation might also be reflected in motor response vigour and eye movements, implicit measures of subjective utility. To examine motor response vigour and visual fixation correlates of option valuation in intertemporal choice, we set up a task where the participants selected an option by pressing a grip force transducer, simultaneously tracking fixation shifts between options. As outlined in our preregistration (https://osf.io/k6jct), we used hierarchical Bayesian parameter estimation to model the choices assuming hyperbolic discounting, compared variants of the softmax and drift diffusion model, and assessed the relationship between response vigour and the estimated model parameters. The behavioural data were best explained by a drift diffusion model specifying a non-linear scaling of the drift rate by the subjective value differences. Replicating previous findings, we found a magnitude effect for temporal discounting, such that higher rewards were discounted less. This magnitude effect was further reflected in motor response vigour, such that stronger forces were exerted in the high vs. the low magnitude condition. Bayesian hierarchical linear regression further revealed higher grip forces, faster response times and a lower number of fixation shifts for trials with higher subjective value differences. An exploratory analysis revealed that subjective value sums across options showed an even more pronounced association with trial-wise grip force amplitudes. Our data suggest that subjective utility or implicit valuation is reflected in motor response vigour and visual fixation patterns during intertemporal choice. Taking into account response vigour might thus provide deeper insight into decision-making, reward valuation and maladaptive changes in these processes, e.g. in the context of neuropsychiatric disorders.

2 Gaussian grip force model Fig B. Parameters of the modelled grip response (mean values per participant and magnitude condition). The handgrip response was modelled with a Gaussian function with 1 term plus a constant (see Eq 10). Amplitude has been normalised to MVC (maximal voluntary contraction). Centroid and width are reported in seconds. Fig C. Within-subject dierences of the parameters of the modelled grip response between the low and high magnitude condition. The handgrip response was modelled with a Gaussian function with 1 term plus a constant (see Eq 10). Amplitude has been normalised to MVC (maximal voluntary contraction). Centroid and width are reported in seconds.
3 Conict based on trial-wise drift rate (DDM) Response conict was also operationalised based on the trial-wise drift rate calculated based on the estimated parameters of the highest-ranked DDM using normalised values (DDM sig-shift ). The posterior distributions of the group-level parameter means for the regression coecients are depicted in Fig D ( -0.05 [N xation shifts]). The Bayes factors provide only anecdotal evidence that the regression coecient for grip force amplitude is greater than zero vs. smaller than zero (BF for β 1 : 1.29), or that the coecients for centroid, width and number of xation shifts are below zero rather than above zero (BF for β 2 : 1.28, BF for β 3 : 1.57, BF for β 4 : 1.72). Since for all βs, the 95% HDIs of the posterior distribution lie neither completely inside nor outside the ROPE, we remain undecided for these regression coecients. The medians of the group-level posterior distributions were as follows: The Bayes factors for all β regression coecients (for amplitude, centroid, and width of the grip response and number of xation shifts) provide only anecdotal evidence for values greater than zero (BF for β 1 : 1.07, BF for β 2 : 0.78, BF for β 3 : 1.02, BF for β 4 : 0.89). We remain undecided for all β coecients, since the 95% HDI of the posterior distribution is neither completely inside nor outside the ROPE (see Fig E).

Sum of larger-later (LL) and smaller-sooner (SS) amounts (model-free)
To analyse the association between motor response vigour, number of xation shifts and total value, we regressed the parameters of the Gaussian grip force model and the number of xation shifts onto the sum of the LL and SS option amounts. The medians of the group-level posterior distributions were as follows (see Fig F): α = 0.51 (intercept), β 1 = 0.53 (amplitude), β 2 = 0.19 (centroid), β 3 = 0.19 (width), β 4 = -1.29 (N xation shifts). The Bayes factor for the regression coecient for peak force provides very strong evidence for values greater than zero vs. smaller than zero (BF for β1: 41.07). The Bayes factor for the coecients for centroid and width provide only anecdotal and moderate evidence, respectively, for values greater than zero vs. smaller than zero (BF for β2: 2.79, BF for β3: 3.04). The Bayes factor for the coecient for number of xation shifts provides extreme evidence for values smaller vs. greater than zero (BF for β4: > 10 308 ). For β1, β2 and β3 we remain undecided, since the 95% HDI of the posterior distribution is neither completely inside nor outside the ROPE. For β4 we reject the null value (95% HDI of posterior distribution entirely outside ROPE). The medians of the group-level posterior distributions were as follows: α = 0.94 (intercept), β 1 = 0.12 (amplitude), β 2 = -0.30 (centroid), β 3 = -0.19 (width), β 4 = -0.56 (N xation shifts) (see Fig G). The Bayes factor for the regression coecient for grip force amplitude provides anecdotal evidence for values greater than zero vs. smaller than zero (BF for β 1 : 2.81). The Bayes factor for the regression coecient for the grip centroid provides strong evidence for values smaller than zero vs. greater than zero (BF for β 2 : 10.40), the Bayes factor for the regression coecient for the width parameter provides moderate evidence for values smaller than zero vs. greater than zero (BF for β 3 : 4.73), and the Bayes factor for the regression coecient for the number of xation shifts provides extreme evidence for values smaller than zero vs. greater than zero (BF for β 4 : 184.48).
Since the 95% HDIs of the posterior distributions for β 1 , β 2 , and β 3 fall neither completely inside nor outside the ROPE, we remain undecided for these three regression coecients. For β 4 we reject the null value (95% HDI of posterior distribution entirely outside ROPE). Posterior distributions of the group-level parameter means. α: intercept, β 1 : coecient for grip force amplitude, β 2 : coecient for grip force centroid, β 3 : coecient for grip force width, β 4 : coecient for xation shift. Horizontal solid lines indicate the 85% and 95% highest density interval. Vertical solid lines indicate x = 0, and vertical dashed lines indicate the lower and upper bounds of the region of practical equivalence (ROPE).

6.2
High magnitude condition The medians of the group-level posterior distributions were as follows: α = 0.99 (intercept), β 1 = 0.53 (amplitude), β 2 = -1.18 (centroid), β 3 = 0.11 (width), β 4 = -0.83 (N xation shifts) (see Fig H). The Bayes factor for the regression coecient for grip force amplitude provides very strong evidence for values greater than zero vs. smaller than zero (BF for β 1 : 60.27). The Bayes factor for the regression coecient for the grip centroid provides extreme evidence for values smaller than zero vs. greater than zero (BF for β 2 : 2181.35), the Bayes factor for the regression coecient for the width parameter provides moderate evidence for values greater than zero vs. smaller than zero (BF for β 3 : 2.19), and the Bayes factor for the regression coecient for the number of xation shifts provides extreme evidence for values smaller than zero vs. greater than zero (BF for β 4 : 593.96). For β 2 and β 4 we reject the null value (95% HDI of posterior distribution entirely outside ROPE). For β 1 we also reject the null value, since the 95% HDI dos not include zero and only 0.63% of the 95% HDI overlaps with the ROPE. For β 3 we remain undecided, since the 95% HDI of the posterior distribution is neither completely inside nor outside the ROPE. Posterior distributions of the group-level parameter means. α: intercept, β 1 : coecient for grip force amplitude, β 2 : coecient for grip force centroid, β 3 : coecient for grip force width, β 4 : coecient for xation shift. Horizontal solid lines indicate the 85% and 95% highest density interval. Vertical solid lines indicate x = 0, and vertical dashed lines indicate the lower and upper bounds of the region of practical equivalence (ROPE).